Vibrational-mechanical properties of the highly-mismatched Cd1−xBexTe semiconductor alloy: experiment and ab initio calculations

The emerging CdTe–BeTe semiconductor alloy that exhibits a dramatic mismatch in bond covalency and bond stiffness clarifying its vibrational-mechanical properties is used as a benchmark to test the limits of the percolation model (PM) worked out to explain the complex Raman spectra of the related but less contrasted Zn1−xBex-chalcogenides. The test is done by way of experiment (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x\le 0.11$$\end{document}x≤0.11), combining Raman scattering with X-ray diffraction at high pressure, and ab initio calculations (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document}x ~ 0–0.5; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document}x~1). The (macroscopic) bulk modulus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 drops below the CdTe value on minor Be incorporation, at variance with a linear \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 versus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document}x increase predicted ab initio, thus hinting at large anharmonic effects in the real crystal. Yet, no anomaly occurs at the (microscopic) bond scale as the regular bimodal PM-type Raman signal predicted ab initio for Be–Te in minority (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document}x~0, 0.5) is barely detected experimentally. At large Be content (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document}x~1), the same bimodal signal relaxes all the way down to inversion, an unprecedented case. However, specific pressure dependencies of the regular (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document}x~0, 0.5) and inverted (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document}x~1) Be–Te Raman doublets are in line with the predictions of the PM. Hence, the PM applies as such to Cd1−xBexTe without further refinement, albeit in a “relaxed” form. This enhances the model’s validity as a generic descriptor of phonons in alloys.

pressure / low-temperature experiment ( =0.11).However, at large Be content (~1) the ab initio bimodal Be-Te Raman signal "relaxes" all the way down to (a slight) inversion -giving rise to an unprecedented crossing of percolation sub-branches in a "Raman frequency vs. " plot.The inverted doublet exhibits a remarkable intensity interplay under pressure, grasped within a linear dielectric approach.Altogether, the  0 -drop at ~0 and the inversion of the Raman signal at ~1 reflect a negative impact of the large bond mismatch on the Cd 1-x Be x Te mechanical-vibrational properties at various length scales and compositions.Yet, the percolation scheme applies as such to Cd 1-x Be x Tealbeit in a "relaxed" form, without further refinement.This enhances the scheme's validity as a generic descriptor of phonons in alloys.
of the extended states forming the host conduction band with a quasi -resonant highly localized impurity state [10][11][12][13][14] .Oxygen likewise induces an intermediate band within the bandgap of O-dilute ZnTe 1-x O x 15,16 and CdTe 1-x O x 17 .No similar outstanding features were detected with Zn 1-x Be xchalcogenides, which therefore received less attention so far. 0 varies linearly with  in Zn 1-x Be x Te 18 , or undergoes just a slight bowing in Zn 1-x Be x Se 19 .More generally, the (quasi) linearity with composition governs all studied critical points of the electronic band structure of Zn 1-x Be x -chalcogenides (considering the direct gaps between the upper valence band and the lower conduction band at the Γ,  and  points -namely  0 ,  1 and  2 , and the corresponding gaps involving the light hole valence band -notably  0 + ∆ 0 and  1 + ∆ 1 , as assigned in Ref. 20 ), for both Zn 1-x Be x Te 21 and Zn 1-x Be x Se 22 .
However, the Zn 1-x Be x -chalcogenides have held a central place in what regards vibrational properties.In early 2000's, pioneering Raman studies [23][24][25] revealed a bimodal signal per bond (1-bond→2-mode) that contested the classical view of a unique mode per bond (1-bond→1-mode) in random zincblende alloys 26 .This was explained in terms of sensitivity of the effective bond force constant () -probed by Raman scattering -to local Be-and Zn-like environments, casted into the percolation model (PM, Ref. 27 and refs.therein).Subsequently, the PM enabled a unified understanding, hitherto missing, of the Raman spectra of II-VI, III-V and IV WMA's with cubic (zincblende, diamond) and hexagonal (wurtzite) structures, suggesting the model's universality 27 .
The bond force constant () and the bond length () are related via a basic rule that the former decreases as the latter is stretched, and vice versa.Referring this to the Zn 1-x Be x -HMA's the variation in Be-related bond force constant (~10%) observed in Raman 25,27 and far-infrared absorption 28 experiments is correlated with a predicted variation in Be-related bond length (~2%, from ab initio calculations 29 ) depending on whether the Be-related bond is in a Be-like or Zn-like environment.
Unfortunately, this bimodal distribution of the Be-related bond length could not be resolved in extended X-ray absorption fine structure (EXAFS) measurements on a synchrotron 30,31 , and is a priori hardly detectable via the pair distribution function in conventional total X-ray scattering experiments 32 ,33 .The same applies a fortiori to the less contrasted WMA's.For instance, the III-V (covalent) Ga 1-x In x As and II-VI (ionic) ZnSe 1-x Te x alloys usually ranked among WMA's despite their significant lattice mismatch (~7%, Ref. 3 ) likewise exhibit a unique bond length per species at a given  value in EXAFS data [34][35][36] .Yet their Raman signal is bimodal per bond -of the percolation type 25,37 .
Hence, EXAFS does not resolve the splitting of the A-C or B-C bond lengths of A 1-x B x C zincblende alloys -HMA's included -due to A-like or B-like local environments and thus yields a basic 1-bond→1-length description 38 , whereas the Raman signal diversifies into a (percolation-type) 1-bond→2-mode pattern.
In a nutshell, the lattice dynamics zooms deeper into the alloy disorder than the lattice relaxation.This is interesting on the fundamental side.
Besides, the PM opens applications.In particular, the phonons being sensitive to the local environment -as formalized within the PM, they can be used to elucidate whether the atom substitution is ideally random or not 27 , the central issue when dealing with alloys.Apart from vibrational spectroscopies, the nuclear magnetic resonance (NMR) seems to be the only one in-house technique capable of addressing such issue quantitatively 39 -an example is given below.Alternatively, one may resort to EXAFS measurements (using a synchrotron) of the second-neigbor distances for the common-atom sublattice (i.e., the Te-Cd-Te and Te-Be-Te ones for Cd 1-x Be x Te) -which differ on account that each bond tends to preserve its natural length in an alloy 35,38 .
In this work, the PM is tested on the emerging Cd 1-x Be x Te HMA that exhibits an even larger bond mismatch ( ∆  ~15%, ∆   3     3 ~36%) than the Zn 1-x Be x -chalcogenides.It is not a priori obvious whether the PM would apply to such special system.In the positive case, it will be instructive to elaborate on specific consequences from the PM, listed below from basic to more advanced ones 40 : 1.Only Be-Te should exhibit a distinct Raman doublet.Being small, Be has more room than Cd to move around in the Te-cage to accommodate the local strain created by the bond mismatch, with concomitant impact on the Raman frequencies being more diversified for Be-Te than for Cd-Te.
2. Out of the two sub-modes within the Be-Te doublet, the softer (harder) one would refer to Be (Cd)-like environments.Consider, e.g., an isolated Cd atom embedded in BeTe.In its vicinity, the short Be-Te bonds suffer a compressive strain due to a competition with the longer Cd-Te ones within the given lattice spacing, hence vibrate at a higher frequency than the bulk-like Be-Te bonds away from Cd.An inverse argumentation applies to CdTe doped with Be.
3. The Be-Te doublet is expected to converge under pressure.This is due to a larger volume derivative of the bond ionicity     ⁄ (with   = 1 −   ) for Be-Te (0.7453) than for Cd-Te (0.407) 3 .Hence, the Be-like environment hardens under pressure faster than the Cd-like environment does, so that thence stemming (softer) Be-Te Raman line within the percolation doublet drifts (upwards) under pressure faster.A classification of II -VI and III-V (WMA's and HMA's) alloys was accordingly suggested in Ref. 27 .
4. This convergence either ends up into a phonon exceptional point at the crossing -resonance (scenario 1), or freely develops into an inverted doublet post resonance (scenario 2), depending on whether the (Be-Te) bond responsible for the vibration doublet is dispersed (self-connects in chains) or matrix-like (self-connects in bulk), respectively.The Raman intensity of the minor mode within the doublet undergoes, correspondingly, an extinction (scenario 1) or enhancement (scenario 2).
More generally, the ambition of this work is an integrated and coherent fundamental study of mechanical properties of the Cd 1-x Be x Te HMA at the macroscopic (via elasticity) and microscopic (sensitive to chemical bonds) scales, using Zn

Results and discussion
The studied samples consist of high-quality / purity Cd  S1b), that seems to be common in alloys, HMA's included 2 .Further structural insight at the microscopic scale is gained via powder (=0.07) 125Te solid-state nuclear magnetic resonance (NMR) measurements 39 .A bimodal NMR pattern (Fig. 1a) distinguishes between two tetrahedral environments for Te among five possible ones depending on the number of Cd and Be nearest neighbors.The NMR peak intensities scale as the fractions of tetrahedral Te-clusters with 4×Cd and (3×Cd, 1×Be) atoms at the vertices, as suggested by the Bernoulli's binomial distribution 39 at =0.07 (Fig. 1a, inset).One notes a practical absence of Te-centered clusters with more Be atoms, consistently with experiment.Altogether the NMR data point towards an ideally random Cd↔Be substitution in Cd 0.93 Be 0.07 Te, presumably valid in all studied samples owing to the close Be contents.
Hence the discussed experimental trends hereafter are presumably intrinsic to random Cd 1-x Be x Tealloying.Additional ( 9 Be and 117 Cd) NMR experiment completing the current ( 125 Te) NMR insight into Cd 0.93 Be 0.07 Te are reported as Supplementary Information (Fig. S4).
linearity seems to be the rule with Be substitution.The (Be, Zn, Cd) substituents involved in (Zn,Cd) 1-x Be x -chalcogenides are nearly iso-electronegative (within few percent), in contrast with dilute nitrides / oxydes that exhibit a large contrast in electronegativity between alloying elements (in the range 25-40%) -the admitted cause 16 for their large (negative)  0 vs.  bowing [12][13][14][15][16] .This might be the reason why the (Zn,Cd) 1-x Be x -HMA's behave like WMA's in what regards their optical properties.
We turn now to mechanical-vibrational properties, independently probed at the macroscopic scale at SOLEIL synchrotron (PSICHÉ beamline), searching for the bulk modulus  0 by high-pressure X-ray diffraction (HP-XRD), and at the microscopic scale by high-pressure Raman scattering (HP-RS), sensitive to the bond force constants, in relation to the raised issues (1-to-4) around the PM.For the sake of consistency, both studies are performed at the same Be content (=0.11).
The  0 -drop is not accidental, due to the quality of fit.The first-order pressure derivative of  0 evaluated at 0 GPa,  0 ′ , coming out in the fit is 4.00 ± 0.15 for Cd 0.89 Be 0.11 Te, nearly matching the CdTe 51 (3.8 ± 0.6) and BeTe (fixed to 4 in Ref. 53 ) values.By adopting for  0 ′ the "optimized" AIMPRO ( 0 ′ =4.7,  0 =40.5 GPa) and SIESTA ( 0 ′ =5.1,  0 =39.7 GPa) values at ~10 at.%Be (see below), the  0 -drop for Cd 0.89 Be 0.11 Te is emphasized (and the quality of fit degraded -not shown).A similar  0 -drop is also evidenced by HP-XRD diffraction with Zn 1-x Be x Te (Fig. S3b, x≤0.21) -using  0 ′ =4 (found relevant for both ZnTe 54 and BeTe 53 parents in experiment) for the fitting (Fig. S3a), hence apparently a common feature of BeTe-based alloys.
The  0 -drop deviates from the (quasi) linear  0 vs.  experimental trend observed with Zn 1-x Be x Se -however, disrupted by a punctual lattice hardening on percolation of the stiff Be-Se bonds 30  -with subscript and superscript referring to the vibrating bond and to the local environment, respectively -separated by ∆ − ~20 cm -1 , the intensities of these modes differing by roughly an order of magnitude.Raman measurements at 0 GPa / 300 K with the red (632.8nm) and blue (488.0 nm) laser lines (nearly resonant with the  0 and / or  0 + ∆ 0 electronic transitions of Be-dilute Cd 1-x Be x Te, Fig. 1b) fail to reveal the Be-Te doublet (Fig. S7).Only one Be-Te mode is visible, at ~390 cm -1 , consistent with the scarce experimental (far-infrared) data in the literature 56 and existing calculations using the Green's function theory 57 , far away from the (TO, LO) CdTe-lattice band (140 -170 cm -1 ).This line is assigned as the upper / main   −  , by analogy with  −  of Zn 1-x Be x Te.The lower / minor  −  band is not visible, presumably screened by the second-order CdTe-lattice signal (2 − ) that emerges as a strong feature nearby, being emphasized / reduced with the red / blue laser excitation.
The conditions for testing the PM are improved by keeping the blue laser line but working at high pressure and low temperature (80 K), that offers a number of benefits.First, the Be-Te signal sharpens due to the increased phonon lifetime.Second, the pressure domain of the native zincblende phase enlarges 58 .Third, the low temperature slows down the formation of Te aggregates under intense laser exposition such as achieved by focusing the laser beam onto a tiny sample placed in a diamond anvil cell -a notorious problem with CdTe-like crystals 59 .The Raman spectra taken in the upstroke up to 4.3 GPa in the native zincblende phase of Cd 0.89 Be 0.11 Te (Fig. 2b) transiently reveal the target lower / minor prior to its extinction at the crossing / resonance, as observed with the reference Be-Te doublet of Zn 0.89 Be 0.11 Te across a similar pressure range (2.3-7.9GPa) 40 .This fits into scenario 1 of the convergence process (cf. the issue 4).
Although the analogy with Zn 89 Be 11 Te is enlightening, it remains limited to grasp the behaviour of Cd 0.89 Be 0.11 Te.Additional support is searched for by calculating the high-pressure ab initio (AIMPRO) Cd 1-x Be x Te Raman spectra at small-to-moderate (~0, 0.5) Be content.However, a limit to pressure is set by the supercells becoming unstable from 10 GPa (~0, not shown) and 15 GPa (~0.5,Fig. S7) onwards.The stability improves at large Be content (~1), also considered to complete an ab initio Raman insight at well-spanned  values across the composition domain (Figs.2c, 2d and 2e).
Paired impurities (forming a duo connected via Te, as schematized in Fig. 2a) in large parent supercells represent the minimal impurity motif offering a clear distinction, in the context of the PM, between "impurity" and "host" vibrations in "domestic" and "foreign" environments (labels -to- in Fig. 2a), hence four situations in total at both ends of the composition domain (~0 -Fig.2c and 𝑥~1 -Fig.2e).The duo-impurity modes are identified via their wavevectors, depending on whether they point along the duo (in-chain, noted  and symbolized by ↔) or perpendicular to it (out-of-chain, noted  and marked ↮, yielding five possible variants 40 ).For the host / dominant bond species, the distinction between "foreign" and "domestic" environments is established through the Raman intensity, being small next to the impurity-duo (close-duo, noted , the "foreign" case) and large away from it (bulk, noted , the "domestic" case).Additional insight at maximum alloy disorder (=0.5 -Fig.2d) using a nominally random Cd 54 Be 54 Te 108 supercell (see methods) completes the ab initio picture.
Ab initio results do reveal an actual Cd-Te percolation doublet for Cd 1-x Be x Te at x~0 (Fig. S6a) and 1 (Fig. S6b), albeit a compact one (Fig. 2a) -cf. the issue 1, with  −  set below  −  -cf. the issue 2, as expected.The frequency gap ∆ − hardly exceeds a few cm -1 (that won't be detectable in experiment) meaning that the Cd-Te vibration is almost blind to the local environment.At ~1 the upper  −  is frozen (not Raman active, the frozen mode -identified by its wavevector -is spotted by an arrow in Fig. S6b) due to a phonon exceptional point being achieved already at 0 GPa -cf. the issue 4. At ~0 the Cd-Te doublet becomes inverted by increasing pressure to 5 GPa (Fig. S6a) -cf. the issues 3 and 4. Altogether, this offers a perfect analogy with the Zn-Te doublet of the reference Zn 1-x Be x Te case 40 .
The analogy between Cd 1-x Be x Te and Zn 1-x Be x Te is not as clear in their common Be-Te spectral range, successively addressed hereafter with Cd 1-x Be x Te at small, intermediary and large Be contents.
At ~0 (Fig. 2c), the Be-duo generates a nominal percolation-type (lower / in-chain in experiment (marked by an asterisk in Fig. 2b), whereas it emerges as a distinct feature in ab initio data (Fig. 2c).This might relate to a basic difference at minor Be content that ab initio calculations run on an "ideal" lattice -verified by the  0 vs.  linearity -whereas the real lattice suffers a massive  0 -drop in experiment (Fig. 1d).
At ~0.5 (Fig. 2d), scenario 1 still applies, as expected -cf. the issue 4. At 0 GPa, the Be-Te Raman In earlier work 60 we have shown that the shape of the upper (best-resolved) TO percolation doublet in a "Raman frequency vs. " plot may vary a lot (parallel branches vs. trapezoidal / triangular distortions) depending on wether the parent TO is dispersive or not.The main arguments are briefly recalled hereafter by focusing on the lower parent− and upper impurity− modes forming the percolation doublet in the parent limit.Only the latter mode is subject to dispersion, not the former one, so that their comparison provides a straightfoward insight into the dispersion effect.
In absence of dispersion (as, e.g., for GaP), the  - frequency gap is governed by the local strain due to the bond mismatch (between, e.g., Ga-As and Ga-P in the case of GaAs 1-x P x ), resulting in parallel branches across the composition domain 60 .The TO mode of CdTe is nearly dispersionless 61 , so that the Cd-Te doublet of Cd 1-x Be x Te actually exhibits such parallelism (Fig. 2a).In case of a positive (resp.
negative) dispersion,  is upward (resp.downward) shifted with respect to  roughly by the magnitude of the dispersion, with concomitant on the - frequency gap being enlargedtrapezoidal distortion -(resp.squeezed -triangular distortion), as observed 60 with ZnSe 1-x S x (resp. Si 1-x Ge x ).
We are mainly interested in the negative TO dispersion (with Cd 1-x Be x Te, see below).In this case an inversion of the percolation doublet occurs if the dispersion effect outweights the effect of the local strain (as observed, e.g., with the Si-Si doublet of Si 1-x Ge x at ~0 -Ref. 60).Such an inversion does not occur in the dilute limit, because, being impurity modes, the  and  forming the percolation doublet at this limit suffer a similar dispersion effect.Since the percolation doublet is inverted in the parent limit but regular in the dilute one, its two sub-branches should cross at a certain composition.Such crossing was not observed yet -not even with Si 1-x Ge x (due to the - degeneracy 60 at ~1).
The TO mode of BeTe exhibits a large negative dispersion 62 (~50 cm -1 ).Accordingly, in both Zn 1-x Be x Te 40 and Cd 1-x Be x Te the Be-Te splitting is smaller in the parent limit (~1, -~7 cm -1 -Ref. 40d ~0 cm -1 -Fig.2d, respectively) than in the dilute one (~0, -~30 cm -1 -Ref. 60and ~45 cm -1 -Fig.2c, respectively).Based on ab initio (SIESTA) calculations done on the Be-Te impurity− mode of Cd 1-x Be x Te (Sec.SII.1)-taken as representative for all (-to-) Be-Te impurity modes -the Be-Te doublet at ~0 (- ) is downshifted by ~11 cm -1 due to the dispersion effect (short vertical arrows in Fig. 2a at ~0).A crude view of the (virtual) Be-Te doublet of Cd 1-x Be x Te due to the sole effect of the local strain, i.e., deprived of dispersion, is reconstructed by drawing parallel Be-Te sub-branches (dashed lines, taken straight in a first approximation) -by analogy with the dispersionless Ga-P doublet of GaAs 1-x P x (Ref. 60) -between the (virtual) Be-Te doublet inferred at ~0 in absence of dispersion and the same doublet attached to the parent TO mode at ~1.
When confronted with ab initio data at ~1 -taking into account blindly the effects of strain and dispersion, the above-derived (virtual) strain-related Be-Te doublet appears to be seriously challenged by the TO dispersion, whether considering Cd 1-x Be x Te or Zn 1-x Be x Te.In the latter case, however, the effect of the local strain dominates so that the ordering of Be-Te branches is nicely preserved across the composition domain 40 , even if the branches do not run exactly parallel (cf. the comparison between the - and - frequency gaps).In Cd 1-x Be x Te the effect of the dispersion achieves maximum at ~1 (long vertical arrow, Fig. 2a) and overwhelms the effect of the local strain.This leads to an inversion of the Be-Te doublet (~1), preceded by the crossing of Be-Te sub-branches (~0.8)-an unprecedented case among all re-examined alloys within the PM so far.
Generally, the small / large Be-Te dispersion effect in Zn 1-x Be x Te / Cd 1-x Be x Te at ~1 reflects a small / large (negative) impact of the local lattice distortions due to the Zn / Cd ↔ Be atom substitution on the Be-Te vibrations (the minimum / maximum Be-Te dispersion effect at ~0 / ~1 in Cd 1-x Be x Tecompare the lengths of arrows in Fig. 2a -can be discussed on the same line).However, Cd 1-x Be x Te is not so much remarkable than Zn 1-x Be x Te with this respect, as the dispersion effect usually achieves maximum for the impurity modes of alloys, even in case of WMA's.The distorted percolation doublets of ZnSe 1-x S x and Si 1-x Ge x were discussed on this basis 60 .The Ga-As impurity mode likewise experiences the same (maximal) dispersion effect whether taken in the lattice-matched Ga ) mechanically-coupled harmonic oscillators (Fig. 2f)ranked in order of frequency, by slightly adapting the approach developped in Ref. 40 -notably using there a simplified form of Eq. ( 7) a -see Sec.SIII.2.The pressure dependence of the parent BeTe oscillator strength is taken into account as done in Ref. 40 .For better visualization of trends, the dielectric study has been moved from dilute (~1) to minor (=0.81)Cd content -further offering a direct comparison with the regular Zn 1-x Be x Te case (referring to Fig. 1c of Ref. 40 ).A small mechanical coupling is used (with characteristic frequency  ′ =50 cm -1 , similar to that used with ZnBeTe ) near the resonance -corresponding to frequency matching of the raw-uncoupled oscillators.At this limit, the mechanical coupling achieves maximum (~20 GPa) and the two Be-Te TO submodes exhibit comparable Raman intensities.A further pressure increase eventually results in a proper doublet inversion (30 GPa, Fig. 2f) -as the oscillators tend to decouple by shifting away from the resonance.Such inversion manifests, in fact, the free coupling of Be-Te oscillators at the resonance in Cd 1-x Be x Te -cf. the issue 4.
The free Be-Te coupling is also observed with Zn 1-x Be x Te 40 (~1), only that the transfer of Be-Te oscillator strength mediated by the mechanical coupling is opposite ( due to inversion of the native Be-Te Raman doublets with respect to Cd 1-x Be x Te at 0 GPa -see above).A further difference relates to the Be-Te convergence rate under pressure at ~1, being fast for Zn 1-x Be x Te (the inversion is completed already at ~10 GPa, Ref. 40 ) and slow for Cd 1-x Be x Te (the inversion is still in progress at the largest tested pressure of 20 GPa in our ab initio data -Fig.2e, being delayed to ~30 GPa in view of our dielectric parametrization of Raman lineshapes -Fig.2f).This reflects different driving forces behind the pressure-induced Be-Te convergence processes, namely the regular     ⁄ -mechanism for Zn 1-x Be x Te -cf. the issue 3, and for Cd 1-x Be x Te just a basic trend for like bonds to behave uniformly under pressure (the local environment becoming less discriminatory at high pressure 40 , as already mentioned).Anyway, the free coupling of the inverted / irregular Be-Te doublet of Cd 1-x Be x Te at large Be content (Figs.2e and 2f) opposes the phonon exceptional point achieved at minor-to-moderate Be content (Figs.2b, 2c and 2d), conforming to scenarii 2 and 1 in the main lines -cf. the issue 4.

Conclusion
Among Be-based highly mismatched alloys (HMA's), Cd 1-x Be x Te achieves maximum contrast in bond properties, exacerbating its vibrational-mechanical properties.As such, Cd 1-x Be x Te is an appealing benchmark to test the limit of the percolation model (PM) that so far provided a unified understanding of the Raman spectra of semiconductor alloys -covering well matched alloys (WMA's) as well as HMA's.
The Cd 1-x Be x Te mechanical-vibrational properties are studied experimentally ( ≤0.11) by addressing the bulk modulus  0 and the effective bond force constants, using high-pressure X-ray diffraction and high-pressure Raman scattering in combination.The discussion of experimental data is supported by high-pressure ab initio (SIESTA, AIMPRO) snapshots at moderate Be contents ( ≤0.3), extended to intermediary (~0.5)and large (~1) Be contents situated beyond the experimental stage.
Cd 1-x Be x Te exhibits degraded mechanical-vibrational properties across the composition domain, at both the macroscopic and microscopic scales.On minor Be incorporation (~0), the bulk modulus suffers a counterintuitive drop below the CdTe value.At large Be content (~1) and ambient pressure, the percolation-type Raman signal of the sensitive Be-Te bond is fully relaxed by the phonon dispersion, down to inversion -an unprecedented case among revisited alloys within the PM so far.
Yet, the percolation scheme is not challenged for all that and basically applies as such to Cd 1-x Be x Te.In fact, the Be-Te bond exhibits a mere bimodal Raman pattern at any composition, and not a more complicated one.Further, the pressure-induced convergence of the Be-Te Raman doublet either ends up into a phonon exceptional point at minor-to-moderate Be content or develops into a free mechanical coupling at large Be content, in line with predictions.This reinforces the status of the PM as a robust (phenomenological) descriptor of phonons in semiconductor alloys.
∆ 1 ,  2 ) on top of  0 are accessed via a direct (model-free) wavelength-per-wavelength inversion of spectrometric ellipsometry data (the sine and cosine of the depolarization angles).
High-pressure powder X-ray diffractograms are recorded on the PSICHÉ (Cd 0.89 Be 0.11 Te) and CRISTAL (Zn 1-x Be x Te, =0.045,0.14 and 0.21) beamlines of SOLEIL synchrotron using radiation wavelengths of 0.3738 Å and 0.485 Å, respectively.The highpressure data are recorded with a similar Chervin type diamond anvil cell 68 (with 300 m in diameter diamond culet) as for the Raman measurements (see below), using, in both cases, Ne and Au as the pressure transmitting medium and for pressure calibration, respectively.The high-pressure X-ray data are treated by using the DIOPTAS 69  scatterers 59 , near-resonant conditions are used to enhance the Raman signal, as best achieved at 300 K and 77 K by using the 632.8 nm line of a helium-neon laser, falling in between  0 and  0 + ∆ 0 , and the 488.0 nm line of an argon laser, near-resonant with  0 + ∆ 0 , respectively.Fair modeling of the Raman signal due to uncoupled or mechanically-coupled TO oscillators is achieved within a linear dielectric function approach, adapted from Ref. 40 (Sec.SIII).
(High-pressure) ab initio insights into the lattice relaxation/dynamics.Three ab initio codes operated within the density functional theory, using pseudopotentials and the local density approximation for the exchange-correlation, are employed, according to need.Reference  0 vs.  curves for Cd 1-x Be x Te at moderate Be content ( ≤0.3) are separately obtained by applying the SIESTA 43,44 and AIMPRO (Ab Initio Modeling PROgram 41,42 ) codes to distinct series of large (64-and 216atom, respectively) fully-relaxed (lattice constant, atom positions, supercell shape) and partiallyrelaxed (preventing any supercell distortion so as to maintain the cubic structure needed for a strict application of the Birch-Murnaghan 51 equation of state) disordered zincblende-type supercells, correspondingly.Each supercell represents a random Cd↔Be substitution, obtained by adjusting the fractions of individual Te-centred tetrahedra to the binomial Bernouilli distribution 39 .At each  value,  0 is estimated by fitting the pressure dependence of the volume unit cell with the Birch-Murnaghan equation of state 51 .Further AIMPRO calculations are done on parent-like supercells containing Be-(~0) or Cd-paired (~1) impurity motifs, searching to imitate the limiting-cases Raman signals due to the non-polar (purely-mechanical) TO's of the host and impurity species, using the formula given by de Gironcoli 70 .In their current versions, the AIMPRO and SIESTA codes do not take into account the long-range electric field accompanying the Raman-active polar LO's.Further simulations thus resorted to QE code 45 , giving access to   (the frequency of the non-polar TO),   (the frequency of the Ramanactive polar LO) and  ∞ (the high-frequency relative dielectric constant, i.e., as defined at  ≫   ) of BeTe and CdTe, calculated for (2×2×2) cubic zincblende-type supercells (64 atoms).From these, the static relative dielectric constant   (defined at  ≪   ) could have been extracted by force of the LST relation 71 , to be further used to estimate the phonon oscillator strengths within the classical form of the relative Cd 1-x Be x Te dielectric function   , used in our simplified analytical expression of the Cd 1-x Be x Te Raman cross section (Sec.SIII).S5a) and ellipsometry (hollow symbols, Fig. S5b).CdTe (Ref. 48) and BeTe (Ref. 20) values taken from the literature are added, for reference purpose.Linear (dashed) trends between parent values are guidelines for the eye.Laser lines used to excite the Raman spectra are positioned to appreciate resonance conditions.Antagonist arrows help to appreciate the shift of electronic transitions by lowering temperature from ambient to liquid nitrogen, by referring to the  0 gap of CdTe Ref. 49 .(c) Pressure dependence of the zincblende (zb), rocksalt (rs) and Cmcm (cm) Cd 0.89Be0.11Telattice constant(s) measured by high-pressure X-ray diffraction (Fig. S1c).(d) The  0 value derived for Cd0.89Be0.11Te in its native zb phase (filled circle) from the corresponding volume vs. pressure dependence (Fig. S1d) is compared with the parent values taken from the literature (filled triangles, Refs. 30,50) and with current ab initio data obtained with the AIMPRO (hollow diamonds) and SIESTA (hollow squares) codes.Corresponding linear -dependencies are shown (dashed lines), for reference purpose.The authors declare no competing interests.

Corresponding author
Correspondence to Olivier Pagès.
0 GPa in absence of mechanical coupling ( ′ =0 cm -1 , Fig. 2a), and to the punctual insight into the pressure dependence of the Be-Te Raman doublet at ~1 achieved by considering a weak mechanical coupling ( ′ =50 cm -1 , Fig. 2f) impacting both the Raman frequencies and intensities.

I.
Structural and optical properties of Be-dilute Cd 1-x Be x Te I.1.
(High-pressure) X-ray diffraction -Structural insight at the macroscopic (lattice) scale Raw X-Ray diffractograms obtained at 0 GPa in laboratory using the CuK radation across the current Cd 1-x Be x Te ( ≤0.11) sample series (Fig. S1a) are characterized by sharp peaks at any composition  value, the sign of a high structural quality.The individual peaks are labelled using the (hkl) Miller indices up to maximal angular deviation.The lattice constant  is found to vary linearly with the composition  (Fig. S1b), a standard feature of semiconductor alloys 2 .
A selection of raw high-pressure X-ray diffractograms taken at increasing pressure on Cd 0.89 Be 0.11 Te at the PSICHÉ beamline of SOLEIL synchrotron using the 0.3738 Å radiation (Fig. S1c) reveal no extra peak besides the regular for a given crystal phase, the sign of a high structural purity.As pressure increases, Cd 0.89 Be 0.11 Te transforms from zincblende (0 GPa, abbreviated zb) to rocksalt (~5.5 GPa, rs) -the two phases coexisting over a rather large pressure domain (~5.5 -9 GPa) -and subsequently to Cmcm (~13 GPa, cm), eventually surviving as a unique phase from ~18 GPa up to the maximum achieved pressure in this study (~24 GPa).The pressure dependence of lattice constants in each Cd 0.89 Be 0.11 Te phase (Fig. 1c) is notably used to estimate the bulk modulus  0 at 0 GPa in the native zincblende phase (Fig. 1d) by fitting the pressure dependence of the volume of the unit cell to the Birch-Murnaghan equation of state 51 (Fig. S1d).S3a and S3b, respectively.The fit is done by fixing the reference volume at 0 GPa to the value obtained by considering a linear dependence of the lattice constant versus  in Zn 1-x Be x Te 46 .The as-fitted  0 (symbols) and  0 ′ values at =(0.045, 0.14, 0.21) are (52.857±0.640,52.846±0.170,52.542±0.150) in GPa (the error bars is within the symbol size) and (3.94±0.18,4.05±0.09,4.03±0.06),respectively.For all mixed crystals  0 ′ remains stable at around 4, found relevant for ZnTe 54 and BeTe 53 .A pronounced deviation from the  0 vs.  linearity (dashed line in Fig. S3b) in the sense of a negative bowing is observed -as in the case of Cd 1-x Be x Te (Fig. 1d) -with a minimal  0 value at 21 at.%Be, quasi matched with the parent ZnTe value 54 -52 GPa, well below the BeTe one 53 -67 GPa.  1a).However, the 9 Be (a) and 113 Cd (b) NMR data related to both substituents are also provided (Fig. S4), for the sake of completeness.A unique (well-defined) feature, reflecting the uniqueness of the local environment (all-Te), is visible in each case, as ideally expected.

I.3. Optical properties -Transmission and ellipsometry in combination
The main Cd 1-x Be x Te electronic interband transitions are determined across the sample series in their -dependence by combining transmission ( 0 ) and ellipsometry ( 1 ,  1 + ∆ 1 ,  2 ) measurements in the visible (Fig. 1b).Selected data (Fig. S5) illustrate how the interband transitions are estimated in practice from the raw spectrometric data at each composition, i.e., via a Tauc plot (transmission data, Fig. S5a -curve, filled symbols in Fig. 1b) or by direct (model free) inversion of the measured depolarization angles giving access to the imaginary part of the dielectric function within the 0.6 -5.5 eV spectral range (ellipsometry data, Fig. S5b, hollow symbols in Fig. 1b).

II
that involves the Grüneisen parameter of the parent TO mode, given by S3 , where  is the hydrostatic pressure and  0 the bulk modulus.
High-pressure ab initio (SIESTA) calculations of the lattice relaxation and of the Γ-projected phonon density of states -that assimilates with the TO Raman spectrum in a crude approximation -done on a large 2×2×2 (64-atom) fully relaxed ( 0 ~2.406Å at ambient pressure) cubic BeTe supercell yield  0 and  ,0 values of 63.7 GPa and 478 cm -1 (nearly matching the AIMPRO values in Figs.1d and 2a), respectively, and further predict a linear increase of the TO frequency with pressure at low values (in the range 0 -20 GPa) at the rate of ~10.05 cm -1 per GPa.The resulting   estimate via Eq.( 2) for the parent BeTe TO mode is ~1.33.
Similar SIESTA calculations done at 0 GPa on a similar zincblende-type Cd 31 Be 1 Te 32 supercell containing a unique Be atom give the Be-Te impurity- mode at ~414 cm -1 (slightly above the experimental   −  one at ~0 -see Fig. 2a) after relaxation (achieved via a Be-Te elongation of ∆~0.063Å with respect to the natural-bulk  0 value -see above).This exceeds by ~10 cm -1 the impurity- frequency due to the sole effect of the local strain given by Eq. ( 1).The difference is due to the (negative) dispersion of the BeTe TO mode, impacting all impurity (-to-) modes (as emphasized by vertical arrows in Fig. 2a), in principle 60 .Such study of the lattice relaxation / dynamics around an isolated Be impurity in CdTe (~0), consistently conducted end-to-end within an ab initio (SIESTA) approach in reference to BeTe (~1), points towards the important role of the phonon dispersion besides the local strain in shaping the Be-Te percolation doublet of Cd  pressure / temperature in the backscattering geometry on non-oriented crystal faces using the red (632.8nm, =0 and 0.5) and blue (488.0 nm, =0.11)laser lines near-resonant with  0 and  0 + ∆ 0 , respectively (Fig. 1b).The Raman signal consists of a quasi-degenerated TO-LO Be-Te impurity mode situated at much higher frequency than the CdTe-lattice TO-LO band (140 -170 cm -1 ).Near-resonance conditions favor the (polar) LO's compared with the (non-polar) TO's via the Fröhlich mechanism S4,S5 .
The LO emphasis is especially pronounced with the red laser excitation, manifested by the strong emergence of the second-order matrix signal (2×  − ).A pure Be-Te TO-insight is searched for at the largest available Be content (=0.11)by exciting a (110)-cleaved crystal face at normal incidence with the less resonant blue laser line, and collecting the scattered light in backscattering in the (TOallowed, LO-forbidden) scattering geometry S5 .
The Raman spectrum at minimal Be content (5 at.%) provides a crude experimental estimate of the Be-Te impurity- frequency in CdTe, i.e., ~390 cm -1 , in close agreement with existing data in the literature 56,57 .Besides, the comparison between the LO-like (non-oriented crystal face) and TO-like (cleaved face) Cd 0.89 Be 0.11 Te Raman spectra resolves a finite Be-Te TO-LO splitting (emphasized by dotted lines, Fig. S7).By decreasing  the lattice constant  increases (Fig. S1b) which distances cations and anions and hence softens the chemical bonds, with concomitant impact on the TO (non-polar) Raman frequencies (scaling as the square roots of the effective bond force constant in a crude description 26 ) being downward shifted.The LO (polar) Raman frequencies "mechanically follow", converging progressively towards the (non-polar) TO's when the bond fractions decrease until the TO-LO degeneracy is achieved in the dilute limits (~0 for Be-Te and ~1 for Cd-Te).An overview of the experimental Cd 1-x Be x Te Raman frequencies is given in Fig. 2a (symbols).Altogether, this leaves ten input parameters in total, out of which six relate to the parent compounds ( ∞, ,Ω  , , ) and four to the alloy taken in its (Cd,Be)-dilute limits.All parameters are determined ab initio, without leaving any adjustable one.The input frequencies (two per TO branch) are derived by implementing a simple ab initio (AIMPRO) protocol onto impurity Cd-duo and Zn-duo motifs (referring to the ,  and  end frequencies in Fig. 2a), the parent  , (bulk TO) frequencies (symbolized iii in Fig. 2a) coming out as by-products.The parent TO-LO splittings together with the parent  ∞, values, needed to estimate the parent oscillator strengths -see methods, are obtained by resorting to QE.
Fair phenomenological modeling of the pressure-induced interplay between Raman intensities is achieved within a linear dielectric approach of the relaxed-inverted Be-Te percolation doublet of Cd 1-x Be x Te at ~1 (Fig. 2f) -apparent in ab initio data (Fig. 2e), by taking into account a (weak) mechanical coupling ( ′ ~50 cm -1 -see main text).A relevant expression for the corresponding Raman cross section has lately been derived -see Ref. 40 and specifically Eq. ( 7) therein.A simplified form is currently used in which the coupling term at the numerator is disregarded compared with the two main terms standing for the raw-uncoupled oscillators.The analysis is further displaced from the Bedilute limit (~1) to minor Be contents (~0.8 in this case) for more convenience (see main text)while artificially preserving the peak frequencies as such.A minimal phonon damping is uniformly taken (1 cm -1 ) for clarity.

Fig. 2a displays
Fig. 2a displays an overview of the Cd-Te and Be-Te Cd 1-x Be x Te TO Raman signals across the composition domain with information on frequency (curves) and intensity (color code) -technical detail is given below -offering a convenient eye-support for the forecoming discussion of the dependence of the Be-Te Raman doublet of Cd 1-x Be x Te.Experimental TO and LO Raman frequencies of pure BeTe taken from the literature 55 are added, for reference purpose.The given overview unveils in advance the main result of this work, namely, an irregular crossing of the two Be-Te "percolation" subbranches (~0.8)contrasting with the regular parallelism of the Cd-Te ones.
−  (marked by an asterisk) on the low-frequency side of the main  −  at ~3.5 GPa, before its partial resorption at ~4.3 GPa.This is consistent with  −  suffering a progressive collapse while converging towards  − −  , upper / out-of-chain  −  ) Raman doublet at 0 GPa with a large separation (∆ − ~35 cm -1 )conforming to the issue 2.Not surprisingly, the corresponding (  −  ,  −  ) doublet in Zn 1-x Be x Te is less resolved (∆ − ~20 cm -1 ) 40 due to the smaller bond ( ∆  , ∆  3   3 )-contrast in Zn 1-x Be x Te (~9%, ~31%) than in Cd 1-x Be x Te (~15%, ~36%).As pressure is increased  −  gets closer to  −  -cf. the issue 3 -and suffers a major collapse, to such extent that both its Raman intensity and ∆ − are halved (Fig. 2c), i.e., the early signs of a phonon exceptional point on the verge of being achieved, in line with scenario 1 -cf. the issue 4. Generally, this finds echo in experimental findings -even though  −  shows up as a mere shoulder on  − signal of Cd 54 Be 54 Te 108 (=0.5)shows up as a unique broad   − band.At 5 GPa, this latter transforms into a compact percolation-type (  −  ,  −  ) doublet subsided on its lowfrequency side.At 10 GPa, the doublet further shrinks and the subsidence is emphasized to such extent that, apparently, only  −  survives, and  −  is killed.This nicely recapitulates the sequence leading to the achievement of a phonon exceptional point -cf. the issue 4. The sequence is interrupted from 15 GPa on, due to the collapse of the zincblende structure in the supercell used, manifested by a departure of bond angles from the nominal tetrahedral value (109°, Fig. S7).At ~1 (Fig. 2e), the situation becomes irregular.While well separated when stemming from the Be-duo (~0), the (  −  ,  −  ) doublet of Cd 1-x Be x Te becomes quasi degenerate (  −  ≡  −  ) at 0 GPa when due to the Cd-duo (~1).Indeed, various minor features composing  −  (marked by asterisks in Fig. 2e) do overlap with the main  −  .In contrast, the ( −  ,  −  ) doublet of the reference Zn 1-x Be x Te case is globally preserved across the composition domain 40 .The quasi degeneracy of the Be-Te Raman doublet of Cd 1-x Be x Te at ~1 from 0 GPa undermines the possibility for scenario 2 to develop under pressure -cf. the issue 4 -offering a novel case study.Under pressure, the   −  and  −  lines, already close at 0 GPa, are forced to further proximity -because the local environment becomes less discriminatory between like bond vibrations under pressure 40 -and hence do couple mechanically.This mediates a transfer of the oscillator strength from the main to the minor mode, directly impacting the Raman intensities.Remarkably, the Be-Te oscillator strength is channeled from high to low frequency in the Cd 1-x Be x Te case (~1, as emphasized by a vertical arrow in Fig. 2e), and not the other way around as observed in the reference Zn 1-x Be x Te (~1) case 40 .This can be explained only if the minor  −  (recipient of oscillator strength) lies below the main   −  (donor of oscillator strength) at 0 GPa.Hence, at 0 GPa the Be-Te doublet of Cd 1-x Be x Te (~1) is inverted relative to its regular Zn 1-x Be x Te counterpart (~1) -and not only degenerated.Specifically, the vibration lines follow (upwards) in the ( −  ,   −  ) orderpay attention to the superscripts, as opposed to the regular ( −  ,  −  ) order with Zn 1-x Be x Te 40 (~1) -cf. the issue 2.
1-x Al x As ( ∆  ~8‰) or lattice-mismatched Ga 1-x In x As ( ∆  ~7%) alloys 63 .At this stage, the inversion of the Be-Te Raman doublet at  ≥0.8 is (qualitatively) explained.Now we examine how the mechanical coupling develops between the inverted Be-Te submodes when forced to (further) proximity by pressure.The discussion is conducted in reference to the uncoupled case represented in Fig.2a.The uncoupled modes of Fig.2a.are modeled by assimilating the TO Raman cross section with the imaginary part of the relative dielectric function   (that captures the   → ∞ divergence characteristic of a purely-mechanical TO)64 .The adopted four-mode {2 × ( − ), 2 × ( − )} description conforms with the current ab initio findings -referring to the end -to- modes.A sensitivity of both bond vibrations to their local (CdTe-and BeTe-like) environments at the first-neighbor scale is assumed by analogy with Zn 1-x Be x Te40 , impacting the Raman intensities.The mechanical bond force constants are linearly interpolated between the parent and impurity ab initio values, leading to quadratic dependencies of the TO frequencies.A uniform broadening (1 cm -1 ) is used, so that the Raman intensities (color code) can be directly compared.The remaining input parameters are determined ab initio (Sec.SIII.2); no adjustable parameters are used.The ab initio frequencies are slightly shifted upwards with respect to the experimental ones (symbols -Fig.2a)-by a few cm -1 for pure CdTe (hollow symbols) and by less than 15 cm -1 for pure BeTe (filled symbols) -due to a generally known bias of the local density approximation, innate to our ab initio calculations, to overbind and hence to overestimate the bond force constants -except for the Be-Te impurity− mode at ~0 (hollow symbols) for which a nearly perfect matching occurs.Fair modeling of the pressure-induced interplay between the ab initio Raman intensities of the two Be-Te submodes forming the irregular-inverted ( −  ,   −  ) percolation doublet of Cd 1-x Be x Te near the crossing of percolation branches (~1, Fig. 2e) can be achieved within a dielectric parametrization of two like ( − − ,  − + 40 ) scaled down by (roughly) an order of magnitude with respect to the TO frequencies (~480 cm -1 ) of the rawuncoupled ( −  ,   −  ) oscillators (whose pressure dependence are represented by straight and dotted lines in Fig. 2f, correspondingly).The small coupling successfully mimics the minimal -but finite -ab initio splitting manifesting the anticrossing (~3 cm -1 , emphasized by paired arrows in Fig. 2f) of the coupled (  − − ,  − + software at PSICHÉ and the DATLAB software -kindly provided by K. Syassen (Max-Planck Institut für Festkörperphysik, Stuttgart, Germany) -at CRISTAL.The  0 value of the native zincblende phase at 0 GPa is obtained by fitting the Birch-Murnaghan's equation of state to the pressure dependence of the unit cell volume 51 .The volume of the unit cell at 0 GPa coming into the cited equation is determined from powder X-ray diffraction measurement done at 0 GPa in laboratory conditions using the CuK radiation.(High-pressure) Raman scattering measurements.High-pressure / low-temperature Raman experiment on Cd 0.89 Be 0.11 Te is done in the backscattering geometry by focusing the laser beam through a ×50 microscope objective with a long working distance at normal incidence onto a 40 µm in diameter spot at the (non-oriented) surface (polished to optical quality) of a tiny monocrystal inserted into a Chervin type diamond anvil cell (described above) set into a Helium flow cryostat system operated at liquid nitrogen temperature.CdTe-based crystals being notoriously poor Raman

Figure 1 
Figure 1  Cd1-xBexTe structural, optical and mechanical properties.(a) CPMG Cd0.93Be0.07Te 125Te NMR signal.The binomial distribution of Te-centered nearest-neighbor (NN) tetrahedon clusters depending on the number of Cd atoms at the vertices in case of a random Cd↔Be substitution is added for comparison (inset).The NMR peaks are labeled accordingly.(b) Composition dependence of the main Cd1-xBexTe electronic transitions measured at room temperature by transmission (filled symbols , Fig.S5a) and ellipsometry (hollow symbols, Fig.S5b).CdTe (Ref.48 ) and BeTe (Ref.20 ) values taken from the literature are added, for reference purpose.Linear (dashed) trends between parent values are guidelines for the eye.Laser lines used to excite the Raman spectra are positioned to appreciate resonance conditions.Antagonist arrows help to appreciate the shift of electronic transitions by lowering temperature from ambient to liquid nitrogen, by referring to the  0 gap of CdTe Ref.49 .(c) Pressure dependence of the zincblende (zb), rocksalt (rs) and Cmcm (cm) Cd 0.89Be0.11Telattice constant(s) measured by high-pressure X-ray diffraction (Fig.S1c).(d) The  0 value derived for Cd0.89Be0.11Te in its native zb phase (filled circle) from the corresponding volume vs. pressure dependence (Fig.S1d) is compared with the parent values taken from the literature (filled triangles, Refs.30,50 ) and with current ab initio data obtained with the AIMPRO (hollow diamonds) and SIESTA (hollow squares) codes.Corresponding linear -dependencies are shown (dashed lines), for reference purpose.

Figure 2 
Figure 2  Cd1-xBexTe vibrational properties.Panels are arranged anti -clockwise -starting from an overview at the top-center (a) -in the sense of increasing  values from left (~0) to right (~1) for direct vertical comparisons of the side panels, i.e., (b) vs. (c) and (f) vs. (e), with a snapshot at intermediary composition inbetween (d).(a) Theoretical overview of the Cd1-xBexTe TO Raman frequencies (curves) and intensities (color of curves) at 0 GPa within a four-mode { 2 × (  −  ) , 2 × ( − ) } description in absence of mechanical coupling between oscillators ( ′ =0).A sensitivity of bond vibrations to first neighbors is assumed by analogy with Zn1-xBexTe 40 .The current TO and LO Raman frequencies (hollow symbols) are indicated.BeTe data taken from the literature 55 are added (filled symbols), for reference purpose.A schematic view of the prototypical parentlike supercell (216-atom) containing one isolated impurity-duo used to generate an ab initio insight into the end (~0,1) TO Raman frequencies of Cd1-xBexTe is inserted.Labels (i) to (iv) refer to in-chain, out-of-chain, nearchain and away-from-chain bond vibrations -in this order, as sketched out.The shape of the Be-Te doublet dictated by the sole effect of the local strain, i.e., in absence of dispersion, is schematically represented by straight-dashed parallel lines.The dispersion effect affecting the impurity modes is emphasized by vertical arrows at ~0,1.(b) High-pressure / low-temperature Cd0.89Be0.11TeRaman spectra taken in the upstroke.The Be-Te signal, modeled via Lorentzian functions (dotted lines) transiently exhibits a minor feature at ~3.5 GPa (marked by an asterisk).(c, d, e) Ab initio (AIMPRO) insights into the pressure dependence of the Be-Te Raman signal in large (216-atom) supercells (c) due to the Be-duo (~0), (d) at intermediary Be content (=0.5)and (e) in presence of the Cd-duo (~1) -giving rise to various local modes (spotted by asterisks).(f) Raman cross section reflecting the pressure-dependence of the irregular-inverted (see text) Be-Te TO Raman doublet at minor Cd content (~0.81) in case of a minor mechanical coupling ( ′ =50 cm -1 ).Straight and dotted lines represent the pressure-dependencies of the frequencies of the raw-uncoupled Be-Te modes behind the coupled ones.In panels (b, c), a color code is used to distinguish between the raw-uncoupled TO's stemming from domestic (red) and foreign (blue) environments.Paired vertical -horizontal arrows (in panels (b -f) emphasize pressure-induced changes in Raman intensity -frequency for a given mode.

Fig. S2
Fig. S2 displays selections of similar high-pressure X-ray diffractograms obtained with Zn 1-x Be x Te at (a) =0.045 and (b) 0.21 at the CRISTAL beamline of SOLEIL synchrotron using the 0.485 Å radiationcompleting the already published =0.14 data 40 taken during the same run of experiment.The related experimental (symbols) volume versus pressure dependencies in the native zincblende phase fitted to the Birch-Murnaghan equation of state 51 (curves) and resulting  0 vs.  variations are displayed in Figs.

I. 2 .
Solid state nuclear magnetic resonance (SS-NMR) -Structural insight at the microscopic (atom) scaleIn an alloy with zincblende structure such as Cd -x Be x Te, the substituent (Cd and Be in this case) and invariant (Te) species are intercalated so a to form a (cubic) tetrahedral arrangement.Hence, Cd and Be exhibit a stable nearest-neighbor environment of four Te atoms at any  value.In contrast the tetrahedral environment of Te diversifies into five variants depending on the number of Be and Cd atoms at the vertices.The five types of Te-centrered tetrahedra are present in the crystal at any  value, with various probabilities depending on , following the binomial Bernoulli's distribution in their -dependence in the ideal case of a random Be↔Cd substitution S1 .The pioneering 125 Te solid-state nuclear magnetic resonance (NMR) measurements performed on Cd 1-x Zn x Te by Zamir et al.39 have demonstrated a sensitivity of the NMR shift to the local environment at the nearest-neighbor scale.Hence, only the NMR data related to the invariant Te species (as opposed to the substitutional Cd and Be ones) of Cd 1-x Be x Te can shed light on the nature of the Cd↔Be atom substitution -the reason for the emphasis on Te in the text (Fig.

. Cd 1 -
x Be x Te lattice relaxation / dynamics -Ab initio insights II.1.Cd 31 Be 1 Te 32 (SIESTA code) -isolated-impurity motif An isolated Be atom in CdTe forms short Be-Te bonds suffering a hydrostatic tensile strain from CdTe corresponding to a large bond length.The Be-Te bond elongation ∆ with respect to the natural bond length in the pure BeTe crystal ( 0 ) softens the Be-Te impurity mode in CdTe -referred to as the impurity- mode in the main text -below the parent BeTe TO frequency ( ,0 ).The shift in TO frequency squared ∆  2 relates to the variation in bond length ∆ via the relation 63,S2 ,

Fig. S6 displays
Fig. S6 displays high-pressure ab initio (AIMPRO) CdTe-like TO Raman spectra due to large (216-atom)fully-relaxed (see methods) cubic Cd 106 Be 2 Te 108 (at 0 and 5 GPa -Fig.S6a) and Cd 2 Be 108 Te 108 (at 0 and 20 GPa -Fig.S6b) supercells containing similar (Be-and Cd) impurity-duos (connected via Te), in support to the discussion of the pressure dependence of the Cd-Te doublet of Cd 1-x Be x Te (main text).The Cd-Te doublet exhibits nearly the same spacing between the relevant (-, ~0) and (-, ~1) Cd-Te modes at both ends of the composition domain.Under pressure the doublets either cross

III. 2 . 2 ⁄( 1 −
Contour modeling of (high-pressure) TO Raman spectra -linear dielectric function approach An overview of the TO Cd 1-x Be x Te Raman frequencies (curves) and intensities (thickness of curves) calculated throughout the composition domain at 0 GPa in absence of mechanical coupling between TO oscillators ( ′ =0, as sketched out) is given in Fig.2a.Such contour modeling of the TO {  (, ) → ∞} Cd 1-x Be x Te Raman spectra in their -dependence is achieved within a four-mode {2 × ( − ), 2 × ( − )} version of the percolation model by calculating {  (,)} -in a crude approximationS6,63  (see main text).At 0 GPa, the non-polar TO's are presumably decoupled and hence are explicitly assigned by specifying both the bond vibration and the local environment (via a subscript and a superscript, respectively), i.e., classical form is used for   (, ) including a linear background electronic contribution  ∞ () at high (visible) frequencies besides the phonon (farinfrared) one, i.e., four oscillators in total (=1 to 4) modeled as -Lorentzian functions.In each Lorentzian, the numerator represents the available amount of oscillator strength per -mode   0 ()thatscales as the parent value (  0 =  ∞, • Ω  2  , , with Ω  2 =  , 2 −  , 2 ) weighted by the oscillator fraction (  -term below), directly impacting the -type TO Raman intensity.The denominator ( , 2 () −  2 −   ) monitors the position of the TO -resonance in its -dependence, given by  , 2 () =   ()   ⁄ (the numerator and denominator referring to the effective mechanical bond force constant of oscillator- and to the reduced atomic mass of the -type chemical bond, respectively), with the phonon damping   (introducing a friction force) fixing the full width at half maximum of the -type Raman peaks (taken minimal in Fig. 2a, i.e., 1 cm -1 , for a clear resolution of neighboring features and direct comparison of the Raman instensities).We assume linear   () vs.  variations -in the spirit of the historical modified-random-element-isodisplacement (1-bond→1mode) model 26 used to describe the Raman spectra of semiconductor alloys, leading to quadratic  , 2 () variations.By analogy with Zn 1-x Be x -chalcogenides 25,40 , a sensitivity of Be-Te vibrations to crystalline environment limited to nearest neighbors is considered.The corresponding 1D-oscillators behind the four TO's (specified in brackets above) can be casted as {( − ), ( − ), ( − ), ( − )}, participating with weights { −  =  • (1 − ),  −  = ) 2 ,  −  =  2 ,  −  =  • (1 − )}.The TO Raman intensities (color code in Fig. 2a) scale accordingly.Hence the two TO submodes forming a given (Cd-Te or Be-Te) doublet exhibit comparable Raman intensities at ~0.5.

Figure S1 
Figure S1  (High-pressure) Cd1-xBexTe ( ≤0.11) X-ray diffraction data.(a) Powder Cd1-xBexTe X-ray diffractograms obtained at ambient pressure in laboratory.(b) Corresponding -dependence of the lattice parameter.The BeTe value, taken from the literature 47 , is added to complete the trend.The linearity is emphasized (dotted line).(c) selection of Cd0.89Be0.11Te-powderX-ray diffractograms obtained at increasing pressure.The individual peaks are labelled via the (hkl) Miller indices of the corresponding diffraction planes in various (zincblende-zb, rocksalt-rs, Cmcm-cm) structural phases.Additional diffraction peaks originate from Au and Ne used for pressure calibration and as the pressure transmitting medium, respectively.(d) Corresponding pressure dependence of the unit cell volume fitted to the Birch-Murnaghan equation of state.

Figure
Figure S3 Zn1-xBexTe bulk modulus.(a) Pressure dependencies of the unit cell volume -as derived from the high-pressure Zn1-xBexTe X-ray diffractograms (partially reported in Fig. S2) -fitted to the Birch-Murnaghan equation of state, including similar data obtained with Zn0.86Be0.14Te in the same run of experiment.(b) Resulting  0 vs.  variations.

Figure
Figure S5 Cd1-xBexTe transmission and ellipsometry data.(a) Cd1-xBexTe Tauc plot (curves) of transmission data (symbols) giving access to  0 .(b) Corresponding ellipsometry data obtained by direct (model free) wavelengthper-wavelength inversion of the sine and cosine of the depolarization angles measured by ellipsometry .The main electronic transitions are indicated.

Figure S6 
Figure S6  High-pressure ab initio (AIMPRO) CdTe-like Raman signals of Cd1-xBexTe generated by impurityduos (~0,1).(a) Cd106Be2Te108.(b) Cd2Be106Te108.Under pressure the CdTe-like branches either cross (as emphasized by a curved arrow) or freeze (the concerned submode is spotted by vertical arrows) at the resonance, as sketched out.

Figure S7 
Figure S7  (High-pressure) ab initio (AIMPRO) insight into the Cd54Be54Te108 lattice relaxation.Pressure dependence of the ab initio bond-angle distribution within the large (216-atom) Cd54Be54Te108 zincblende-type supercell optimized to a random Ce↔Be substitution bonds used to calculate the ab initio (AIMPRO) Raman spectra discussed in the main text (Fig. 2d).The nominal angle value in the zincblende structure (109°, dotted line) is indicated, for reference purpose.A significant deviation from 15 GPa onwards is emphasized (69°, dotted line).

Figure
Figure S7 Experimental Cd1-xBexTe ( ≤0.11) Raman spectra at ambient conditions.LO-like Cd1-xBexTe Raman spectra taken in the backscattering geometry on unoriented crystal faces polished to optical quality in nearresonant conditions with the red (632.8nm) and blue (488.0 nm) laser lines (Fig. 1b).A pure-TO Cd0.89Be0.11TeRaman spectrum taken with the 488.0 nm laser line in the backscattering geometry at normal incidence onto a (110)-cleaved face is added, for comparison.Paired dotted lines mark a finite TO -LO splitting at =0.11.
45,44e x Te40as a suitable reference -based on proximity of Cd and Zn in the periodic table.Specifically, we combine high-pressure X-ray diffraction measurements on single crystals at the PSICHÉ and CRISTAL beamlines of SOLEIL synchrotron, in search for the macroscopic bulk modulus ( 0 ), with high-pressure Raman scattering measurements (on the same samples), probing the effective bond force constants in line with the above raised issues (1-to-4) around the PM.The discussion of Cd 1-x Be x Te experimental data is supported by high-pressure ab initio snapshots of the lattice relaxation, notably to determine the equation of state from which  0 is issued, and of the lattice dynamics, with special attention to the Raman frequencies and intensities.Additional ab initio calculations are implemented to cover  values beyond the experimental range (currently limited to 11 at.%Be).Various ab initio codes are used, i.e., AIMPRO41,42(Ab Initio Modeling PROgram), SIESTA43,44and QE45(Quantum Expresso), depending on need -as specified in the course of the discussion.
Besides, we briefly test by ellipsometry and transmission if the  0 vs.  dependency is (quasi) linear, like with Zn 1-x Be x -HMA's, or significantly deviates from linearity, like with N/O-dilute HMA's.It is a matter to appreciate on an experimental basis whether HMAlloying with second-row elements (Be, N, O) is virtuous for  0 (in that it generates a smooth linear-like  0 vs.  variation) only in case of Zn↔Be substitution (as discussed above) -for whatever reason, or is a more general rule with Be.